1. Field of the Invention
The present application relates to nuclear medical imaging, and more particularly to methods and apparatus for reconstructing nuclear medical images from three-dimensional PET acquisition data using linograms.
2. Related Art
Gamma cameras, also referred to as nuclear imaging cameras, radioisotope cameras, scintillation cameras and Anger cameras, are used to measure gamma radiation emitted by a body under examination. By measuring the energy and the location of the gamma ray emissions, an image representative of the gamma radiation emitted from the body under examination can be created.
In the field of positron emission tomography (PET), opposing detectors detect the emission from annihilation of a positron of a pair of simultaneous gamma photons traveling in opposite directions. Typically, a large number of scintillation detectors (e.g., scintillation crystal detectors) are arranged in rings. The PET electronics determine when two oppositely arranged detectors produce an event signal at essentially the same time, indicating that a pair of annihilation gamma rays has been detected. The emitted positron that was the source of the pair of gamma rays is considered to be located on a line of response (LOR) connecting the locations on each detector where each gamma ray was detected. The principle is illustrated by FIG. 1, where four detectors are shown for simplicity of explanation.
The emission source causes coincidences between detectors A and D, and between B and C, but not between A and C, or B and D. The x and y coordinates of the source (see FIG. 2) are determined by the crossing point of the active LORs connecting the points on each detector where the coincident gammas were detected. The z coordinate is the coordinate of the plane in which the detectors all lie. Through the use of hundreds of detectors in each ring, this triangulation principle can be used to build an image via the well-studied science of tomographic reconstruction.
In PET, one attempts to reconstruct three dimensional objects by using measurements of line integrals through the measurement space. FIG. 2 shows as an example one small part of the image, a source point that can be characterized by three coordinates (xs, ys, zs). The PET reconstruction problem is to measure the emission intensity of all such points in the image measurement space.
In practice, instrument designers increase the z sampling by operating the detectors three dimensionally. Coincidences are recorded between detectors that are not in a common plane. If one detector has coordinate z1 and a coincident detector has coordinate z2, the simplest approximate formula for the source z coordinate is zs=(z1=z2)/2. This approximation has been called single-slice rebinning. The well-known Fourier rebinning method or FORE, is another approach, and is still used in most of the clinical 3D PET performed around the world.
Grouping lines of response into a plane of constant z, with techniques like the ones mentioned in the last paragraph, leads to faster reconstructions. Two-dimensional reconstruction methods are normally much faster than 3D reconstructions. The speed advantage is important because current PET image reconstruction uses iterative techniques, in which image fidelity tends to improve as one uses more iterations, yet one is forced to stop the iterations before convergence is attained, so that the image can be delivered to the physician in an acceptable amount of time.
It is well-known that the ML-EM (Maximum Likelihood Expectation Maximization) (or simply “EM”) iterative algorithm provides very good PET image reconstruction, but it has been considered too slow for clinical use. A primary drawback for using the ML-EM method is that it requires, in principle, an infinite number of cycles, or iterations, to converge to the answer. The subsequent development of acceleration techniques such as Ordered Subset Expectation Maximization (OSEM), and the development of Fourier rebinning for transforming 3D PET sinograms into 2D sinograms, made iterative reconstruction clinically feasible by allowing approximations to be used in the algorithm. However, factors such as convergence and the limit-cycle effect still presented arguments in favor of EM.
The present inventors have previously provided a method combining EM with the Approximate Discrete Radon Transform (ADRT), as disclosed by M. L. Brady in “A fast discrete approximation algorithm for the Radon transform,” SIAM J. Comput., Vol. 27, no 1, p 107-119, February 1998. See Published U.S. Patent Application No. 2003/0190065, published Oct. 9, 2003, incorporated herein by reference in its entirety. This new method allowed EM reconstructions to be accelerated by orders of magnitude, thereby generating results in about the same time as OSEM.
However, there remains a need in the art to accelerate image reconstruction calculations even further, and to provide image reconstruction methods for 3D PET images.